1. Field of the Invention
The present invention relates to a synthesized digital filter made from analog components or optical components.
2. Description of Related Art
The basic function of digital filters is to manipulate a sampled set of data and produce a new sampled set of data. The digital filter can manipulate data using convolution techniques if the processing is restrained to the time domain. Or, the digital filter can manipulate data using Z-transform techniques if the processing is restrained to the frequency domain. Regardless of how the data is manipulated, all digital filters are implemented as either a Finite Impulse Response (FIR) Filter or an Infinite Impulse Response (IIR) Filter. The issue of which type of digital filter should be used for a particular design depends upon the nature of the problem and the specification of the desired response.
A digital filter 100 can be based on the following well known difference equation #1:                               y          ⁡                      (                          n              ·              T                        )                          =                                            ∑                              i                =                0                            r                        ⁢                                          L                i                            ·                              x                ⁡                                  (                                                            n                      ·                      T                                        -                                          i                      ·                      T                                                        )                                                              -                                                    ∑                                  j                  =                  1                                            m                        ⁢                                          K                j                            ·                              y                ⁡                                  (                                                            n                      ·                      T                                        -                                          j                      ·                      T                                                        )                                                                                        (        1        )            where:                T=Sampling period.        n=An integer to establish the time position of each sample.        x(nT)=Discretized or sampled value of input signal (102).        y(nT)=Discretized or sampled value of output signal (104).        r=The number of input sample coefficients.        m=The number of output sample coefficients.        Li=Gain (tap weights) for the input sample data (106).        Kj=Gain (tap weights) for the output sample data (108).FIG. 1 is a block diagram illustrating a graphical representation of an IIR digital filter 100 based on equation #1. It is understood that if m is set equal to zero, then the digital filter is a FIR digital filter because the computed output y(n) is dependent on the current input sample x(n) and past input samples x(n−i). If m is not zero, then the digital filter is an IIR filter because the computed output y(n) is dependent upon the last computed output y(n−j), as well as the current input sample x(n) and past samples x(n−i).        
A digital filter 200 can also be based on the following well known difference equation #2 which is created by applying a z-transform to equation #1:                               H          ⁡                      (            z            )                          =                                            Y              ⁡                              (                z                )                                                    X              ⁡                              (                z                )                                              =                                                    ∑                                  i                  =                  0                                r                            ⁢                                                L                  i                                ·                                  z                                      -                    i                                                                                      1              +                                                ∑                                      j                    =                    1                                    m                                ⁢                                                      K                    j                                    ·                                      z                                          -                      j                                                                                                                              (        2        )            where:                H(z)=Z-transform of filter response.        Y(z)=Z-transform of output response (212).        X(z)=Z-transform of input response (202).        r=The number of input sample coefficients.        m=The number of output sample coefficients.        Li=Gain (tap weights) for the input sample data (206).        Kj=Gain (tap weights) for the output sample data (208).        z−i=Z-transform of the discretized version of an input delayed by i samples (204).        z−j=Z-transform of the discretized version of an output delayed by j samples (210).        
FIG. 2 is a block diagram illustrating a direct graphical representation of an IIR digital filter 200 based on equation #2. As can be appreciated, the direct graphical representation of the IIR digital filter 200 based on equation #2 avoids the complicated inverse z-transform associated with the IIR digital filter 100 based on equation #1. As can also be appreciated, the direct graphical representation of the IIR digital filter 200 requires the use of a relatively large number of r+m unit delays shown as z−1 elements 204 and 210. The requirement of using a relatively large number of z−1 unit delay elements 204 and 210 can be significantly reduced in many applications by re-arranging various elements and moving the z−1 unit delay elements 204 to produce yet another graphical representation of the IIR digital filter 200. A second graphical representation of an IIR digital filter 300 based on equation #2 is shown in FIG. 3. Even though the IIR digital filter 300 is shown with the assumption that m is larger than r in equation #2, it could be easily drawn for the case where r is larger than m.
The traditional way to implement either of the topologies associated with IIR digital filter 100, 200 and 300 is to use at least three digital components including: (1) a signal processing unit (SPU); (2) an analog-to-digital (A/D) converter; and (3) a digital-to-analog (D/A) converter. It is well known that the operating speeds of these digital components directly relate to and limit the operating speed of the IIR digital filter 100, 200 and 300. Unfortunately, as the operating speeds of these digital components increase so does their size, cost and power dissipation. Accordingly, there is a need for a digital filter that is implemented with non-digital components which enables a break through the speed barrier and also lowers the cost, size and power dissipation associated with the digital components used to implement the traditional digital filter. This need and other needs are satisfied by the synthesized digital filter of the present invention.